few_shots: Example:
Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
E. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
F. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.


Thought: In this problem, students learn to recognize equivalent fractions. That is, three laps around the playground is 3/12 mile, which is equivalent to 1/4, which is one lap around the school.
Answer: B

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000212

4
options: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Understand independence and conditional probability and use them to interpret data.

Investigate chance processes and develop, use, and evaluate probability models.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Investigate patterns of association in bivariate data.

Interpret linear models.

Use random sampling to draw inferences about a population.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Draw informal comparative inferences about two populations.

Understand and evaluate random processes underlying statistical experiments.

Calculate expected values and use them to solve problems.

Use probability to evaluate outcomes of decisions.

Summarize, represent, and interpret data on a single count or measurement variable.

Develop understanding of statistical variability.

Summarize and describe distributions.
problem_activity: Activity
In this activity, students continue to identify points on a scatter plot as representatives of a single month when two variables are measured. Students are also asked to explain the meaning of some abstract points in the context of the problem and identify when it does not make sense to extrapolate information from the graph based on the context (MP2).
Monitor for students who understand that 60 degrees Celsius is unreasonable for an average monthly temperature in most parts of the world, as well as those who identify the trend to predict negative sales which does not make sense in this context either.
Launch
Arrange students in groups of 2. Allow students 5 minutes quiet work time followed by 5 minutes partner discussion and whole-class discussion.
Ask students to predict what a scatter plot might look like when the temperature is along the
\(x\)
-axis and the sales of coats at a store is along the
\(y\)
-axis.
Representation: Internalize Comprehension.
Demonstrate and encourage students to use color coding and annotations to highlight connections between representations in a problem. For example, ask students to use the different colors to represent and annotate temperature and coat sales in the graph and table.
Supports accessibility for: Visual-spatial processing
Student Facing
A clothing store keeps track of the average monthly temperature in degrees Celsius and coat sales in dollars.
| temperature (degrees Celsius) | coat sales (dollars) |
|-------------------------------|----------------------|
|              -5               |        1,550         |
|              -3               |        1,340         |
|               3               |        1,060         |
|               8               |        1,070         |
|              15               |         680          |
|              21               |         490          |
|              23               |         410          |
|              21               |         510          |
|              17               |         600          |
|              11               |         740          |
|               6               |         940          |
|              -2               |        1,390         |
[IMG]
What does the point
\((15, 680)\)
represent?
For the month with the lowest average temperature, estimate the total amount made from coat sales. Explain how you used the table to find this information.
For the month with the smallest coat sales, estimate the average monthly temperature. Explain how you used the scatter plot to find this information.
If there were a point at
\((0, A)\)
what would it represent? Use the scatter plot to estimate a value for
\(A\)
.
What would a point at
\((B, 0)\)
represent? Use the scatter plot to estimate a value for
\(B\)
.
Would it make sense to use this trend to estimate the value of sales when the average monthly temperature is 60 degrees Celsius? Explain your reasoning.
Student Response
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Activity Synthesis
​The purpose of the discussion is for students to understand that each point in the graph represents a single month in which two measurements are made. Select students to share their responses, including those identified for the last problem.
Consider asking some of the following questions:
“When discussing functions, what is a point of the form
\((0,A)\)
called? What about a point of the form
\((B,0)\)
?” (The
\(y\)
-intercept. The
\(x\)
-intercept.)
“In a scatter plot is there a
\(y\)
-intercept?” (It depends on the context. For some situations, it may not make sense for the variable represented along the
\(x\)
-axis to be zero. For example if the variable is the height of a building. On other situations, there may be more than one point along the
\(y\)
-axis. For example, in a situation like the one in the task, there may be multiple months where the average temperature is 0 degree Celsius.)
“When the average monthly temperature goes up, what seems to be happening to sales?” (They are decreasing.)
Writing, Speaking: MLR1 Stronger and Clearer Each Time.
Use this routine to give students a structured opportunity to revise and refine their response to the last question. Ask each student to meet with 2–3 other partners in a row for feedback. Provide students with prompts for feedback that will help students strengthen their ideas and clarify their language (e.g., “Can you give an example?”, “Why do you think…?”, “How do you know…?”, etc.). Students can borrow ideas and language from each partner to strengthen their final version.
Design Principle(s): Optimize output (for explanation)


correct_option_index: 4